Don't they give you a discount if you bring your own thermos?
Just looked it up:
Reusable Cups
Reducing the environmental impact of our cups depends on the success of two interrelated efforts: developing recyclable cup solutions and dramatically increasing our customers’ use of reusable cups. A lot of our customers are also working to reduce their own environmental impact even as we are. To help them help us, we offer a 10-cent discount in the U.S. and Canada to encourage customers to use their own reusable mugs or tumblers for their beverages. Customers staying in a store can also request that their beverages be served in a ceramic mug. Every paper cup saved helps keep our forests intact. (Learn more about deforestation from our friends at Conservation International.)
http://www.starbucks.com/responsibil...ment/recycling
So get yourself a travel mug designed for cycling, and ditch the paper. If you drink Starbucks every day, the discount would pay for the mug in under a year.